At the 1984 Winter Olympic Games in Sarajevo he won the gold medal in the 20 km individual.

In addition he won silver in the 10 km sprint and bronze with the West German relay team.

Previously at the 1980 Winter Olympic Games in Lake Placid he won a relay bronze medal and at the 1988 Winter Olympic Games in Calgary the relay team won silver.

Angerer won twice at the Holmenkollen ski festival biathlon competition with wins in the 20 km individual in 1984 and 1985.

Subsequently, Angerer tested positive for a doping offence that turned out to be the result of a flu remedy.